1. <=> \(\left(3x+2\right)^3-\left(\left(3x\right)^3+2^3\right)=0\)
<=> \(\left(\left(3x\right)^3+2^3+3\left(3x+2\right).3x.2\right)-\left(\left(3x\right)^3+2^3\right)=0\)
<=>3 (3x + 2) . 3x.2 = 0
<=> (3x + 2 ) . x = 0
<=> x = -2/3 hoặc x = 0
2. Tương tự
1
\(\left(3x+2\right)^3-\left[\left(3x\right)^3+2^3\right]=0\)
\(\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot2+3\cdot3x\cdot2^2+2^3-\left(3x\right)^3-2^3=0\)
\(54x^2+36x=0\)
\(18x\left(3x+2\right)=0\)
\(\orbr{\begin{cases}x=0\\3x+2=0\end{cases}}\)
\(\orbr{\begin{cases}x=0\\x=\frac{-2}{3}\end{cases}}\)
2
\(\left(2x+1\right)^3-\left[\left(2x\right)^3-1^3\right]=0\)
\(\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2+1^3-\left(2x\right)^3-1^3=0\)
\(12x^2+6x=0\)
\(6x\left(2x+1\right)=0\)
\(\orbr{\begin{cases}x=0\\2x+1=0\end{cases}}\)
\(\orbr{\begin{cases}x=0\\x=\frac{-1}{2}\end{cases}}\)
1. ( 3x + 2 )3 - ( 3x + 2 ) ( 9x2 - 6x + 4 ) = 0
<=> ( 3x + 2 ) [ ( 3x + 2 )2 - ( 9x2 - 6x + 4 ) ] = 0
<=> ( 3x + 2 ) ( 9x2 + 12x + 4 - 9x2 + 6x - 4 ) = 0
<=> ( 3x + 2 ) 18x = 0
<=> \(\orbr{\begin{cases}3x+2=0\\18x=0\end{cases}}\)<=>\(\orbr{\begin{cases}x=-\frac{2}{3}\\x=0\end{cases}}\)
2. ( 2x + 1 )3 - ( 2x + 1 ) ( 4x2 - 2x + 1 ) = 0
<=> ( 2x + 1 ) [ ( 2x + 1 )2 - ( 4x2 - 2x + 1 ) ] = 0
<=> ( 2x + 1 ) [ 4x2 + 4x + 1 - 4x2 + 2x - 1 ) ] = 0
<=> ( 2x + 1 ) 6x = 0
<=> \(\orbr{\begin{cases}2x+1=0\\6x=0\end{cases}}\)<=> \(\orbr{\begin{cases}x=-\frac{1}{2}\\x=0\end{cases}}\)
1. ( 3x + 2 )3 - ( 3x + 2 )( 9x2 - 6x + 4 ) = 0
<=> ( 3x + 2 )[ ( 3x + 2 )2 - ( 9x2 - 6x + 4 ) ] = 0
<=> ( 3x + 2 )( 9x2 + 12x + 4 - 9x2 + 6x - 4 ) = 0
<=> ( 3x + 2 ).18x = 0
<=> \(\orbr{\begin{cases}3x+2=0\\18x=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{2}{3}\\x=0\end{cases}}\)
2. ( 2x + 1 )3 - ( 2x + 1 )( 4x2 - 2x + 1 ) = 0
<=> ( 2x + 1 )[ ( 2x + 1 )2 - ( 4x2 - 2x + 1 ) ] = 0
<=> ( 2x + 1 )( 4x2 + 4x + 1 - 4x2 + 2x - 1 ) = 0
<=> ( 2x + 1 ).6x = 0
<=> \(\orbr{\begin{cases}2x+1=0\\6x=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=0\end{cases}}\)
1,\(\left(3x+2\right)^3-\left(3x+2\right)\left(9x^2-6x+4\right)=0\)
\(\left(3x+2\right)\left[\left(3x+2\right)^2-\left(9x^2-6x+4\right)\right]=0\)
\(\left(3x+2\right)\left(9x^2+12x+4-9x^2+6x-4\right)=0\)
\(\left(3x+2\right)18x=0\)
\(\Rightarrow\orbr{\begin{cases}3x+2=0\\18x=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-\frac{2}{3}\\x=0\end{cases}}\)
2,\(\left(2x+1\right)^3-\left(2x+1\right)\left(4x^2-2x+1\right)=0\)
\(\left(2x+1\right)\left[\left(2x+1\right)^2-\left(4x^2-2x+1\right)\right]=0\)
\(\left(2x+1\right)\left(4x^2+4x+1-4x^2+2x-1\right)=0\)
\(\left(2x+1\right)6x=0\)
\(\orbr{\begin{cases}2x+1=0\\6x=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=0\end{cases}}}\)
